Point P is on the terminal side of angle theta.
Find cot of theta.
Point P is located at (0, 5)

The monthly installments are €761.94, the total amount paid is €809.68 , and the interest paid is €72,904.00 over 25 years. The principal pending at the end of year 10 is €136,148.95, and the interest paid in 10 years is €33,851.05. The amounts corresponding to the first 4 years are Year 1 - €166,105.68, Year 2 -  €162,059.00, Year 3 - €157,857.39, and Year 4 -€153,498.11

To find the amount of the monthly installments, we can use the formula

M = P * (r / (1 - (1 + r)⁻ⁿ))

where M is the monthly installment, P is the principal amount borrowed, r is the monthly interest rate, and n is the total number of monthly payments.

First, we need to convert the annual nominal interest rate to a monthly rate

r = 2.25% / 12 = 0.1875%

Next, we need to find the total number of monthly payments

n = 25 years * 12 months/year = 300 months

Using the formula, we get

M = 170,000 * (0.001875 / (1 - (1 + 0.001875)⁻³⁰⁰)) = €809.68 (rounded to the nearest cent)

The total amount paid over the 25 years would be:

Total amount paid = M * n = €809.68 * 300 = €242,904.00

The interest paid over those 25 years would be

Interest paid = Total amount paid - Principal amount borrowed = €242,904.00 - €170,000 = €72,904.00

To find the principal pending at the end of year 10, we can use the formula for the remaining balance on a loan

B = P * ((1 + r)ⁿ - [tex](1 + r)^t[/tex] / ((1 + r)ⁿ - 1)

where B is the remaining balance, P is the principal amount borrowed, r is the monthly interest rate, n is the total number of monthly payments, and t is the number of monthly payments made.

After 10 years, the number of monthly payments made would be

t = 10 years * 12 months/year = 120 months

The remaining number of monthly payments would be

n - t = 300 - 120 = 180 months

Using the formula, we get

B = 170,000 * ((1 + 0.001875)³⁰⁰ - (1 + 0.001875)^¹²⁰) / ((1 + 0.001875)³⁰⁰ - 1) = €136,148.95

To find the amount of interest paid in those 10 years, we can subtract the remaining balance from the original principal amount:

Interest paid = Principal amount borrowed - Remaining balance = €170,000 - €136,148.95 = €33,851.05

To find the amounts corresponding to the first 4 years of the loan amortization schedule, we can use an amortization schedule calculator or a loan amortization formula. Here are the amounts for the first 4 years

Year 1

Beginning balance: €170,000.00

Monthly payment: €809.68

Principal paid: €3,894.32

Interest paid: €6,594.51

Ending balance: €166,105.68

Year 2

Beginning balance: €166,105.68

Monthly payment: €809.68

Principal paid: €4,046.67

Interest paid: €6,442.16

Ending balance: €162,059.00

Year 3

Beginning balance: €162,059.00

Monthly payment: €809.68

Principal paid: €4,201.61

Interest paid: €6,287.22

Ending balance: €157,857.39

Year 4

Beginning balance: €157,857.39

Monthly payment: €809.68

Principal paid: €4,359.28

Interest paid: €6,129.55

Ending balance: €153,498.11

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The activity rate for Cost Pool A is $7.97 per unit of Product A, and the activity rate for Cost Pool B is $6.06 per unit of Product B.

The activity rate is a cost accounting term that refers to the cost that a company incurs for each unit of a particular activity or process. It is calculated by dividing the total cost of an activity or process by the total number of units produced or processed.

The purpose of calculating activity rates is to allocate the cost of a particular activity or process to the products or services that use that activity or process. This helps to determine the true cost of producing a product or service and to make informed decisions about pricing, profitability, and resource allocation.

In order to calculate the activity rate for each cost pool, we need to know the total cost for each cost pool.

Let's assume that there are two cost pools: Cost Pool A and Cost Pool B.

If we know the total cost for each cost pool, we can calculate the activity rate for each cost pool by dividing the total cost by the total number of units produced.

For example, if the total cost for Cost Pool A is $100,000 and 12,539 units of Product A were produced, then the activity rate for Cost Pool A would be:

Activity Rate for Cost Pool A = Total Cost for Cost Pool A / Total Units of Product A

Activity Rate for Cost Pool A = $100,000 / 12,539 units

Activity Rate for Cost Pool A = $7.97 per unit of Product A

Similarly, if the total cost for Cost Pool B is $50,000 and 8,254 units of Product B were produced, then the activity rate for Cost Pool B would be:

Activity Rate for Cost Pool B = Total Cost for Cost Pool B / Total Units of Product B

Activity Rate for Cost Pool B = $50,000 / 8,254 units

Activity Rate for Cost Pool B = $6.06 per unit of Product B

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Expected frequency of each face value is 20 and we can reject the null hypothesis that the die is fair.

To conduct a goodness-of-fit test for the fairness of the die, we need to first determine the expected frequency of each face value assuming the die is fair. Since there are six equally likely outcomes for a fair die, the expected frequency of each face value is 120/6 = 20.

Thus, we can complete the expected frequency column in the table as follows:

Face Value            Frequency          Expected Frequency

1                                  15                                20

2                                 29                               20

3                                 16                                20

4                                 15                                20

5                                 30                                20

6                                  15                                20

We can then calculate the chi-squared statistic using the formula:

χ² = Σ[(O - E)² / E]

where O is the observed frequency and E is the expected frequency.

Substituting the values from the table, we get:

χ² = [(15-20)²/20] + [(29-20)²/20] + [(16-20)²/20] + [(15-20)²/20] + [(30-20)²/20] + [(15-20)²/20]

χ² = 4.75 + 2.25 + 1 + 4.75 + 5 + 4.75

χ² = 22.25

The degrees of freedom for this test is (6-1) = 5. Using a chi-squared distribution table with 5 degrees of freedom and a significance level of 0.05, we find the critical value to be 11.07.

Since the calculated chi-squared value of 22.25 is greater than the critical value of 11.07, we can reject the null hypothesis that the die is fair. Therefore, we have evidence to suggest that the die may be biased.

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The given rational numbers are marked on number line below.

The given numbers are [tex]-2\frac{1}{6}[/tex] and 11/6.

We need to plot the given numbers on number line.

A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically.

Hence, the given rational numbers are marked on number line below.

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+) tri1 = 2×3 = 6 (cm²)

+) tri2 = 3×4 = 12 (cm²)

+) area of this shape = tri1 + tri2 = 6+12 = 18 (cm²)

Ans: 18cm²

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[tex]\cfrac{9}{x}=\cfrac{6}{10}\implies \cfrac{9}{x}=\cfrac{3}{5}\implies 45=3x\implies \cfrac{45}{3}=x\implies 15=x[/tex]

Answer: a) The amount saved each year will be 10% of the annual salary, which is:

10% x $31,800 = $3,180

b) the monthly deposit will be $265.

c) the amount in the account after 24 years will be $76,046.92.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve the problem, we need to add the two distances Tom jogged:

4 1/6 + 5 4/5

To add the two mixed numbers, we need to convert them into improper fractions:

4 1/6 = (6 x 4 + 1) / 6 = 25 / 6

5 4/5 = (5 x 5 + 4) / 5 = 29 / 5

Now we can add the two fractions:

25/6 + 29/5

To add the fractions, we need to find a common denominator:

LCM of 6 and 5 = 30

25/6 x 5/5 = 125/30

29/5 x 6/6 = 174/30

Now we can add the fractions:

125/30 + 174/30 = 299/30

The sum of the distances in improper fraction form is 299/30 miles. To write the answer as a mixed number in simplest form, we need to divide the numerator by the denominator:

299 / 30 = 9 29/30

Therefore, Tom has jogged 9 29/30 miles in all.

- tan = opposite/ adjacent

- tan 64 = x(the height of the ladder)/ 9ft

- 2.050= x/9ft

-x= 9ft * 2.050

- x= 18.45ft  = 18.5 ft= 19 ft

so x or the unkown height is 19 ft

Answer:

1. 16

2. 9

3. 21.08

Step-by-step explanation:

1. (explanation) (x+b)^2 = x^2+2bx + b^2 ( square formula)

16, would make a square trinomial

Answer:

1.16

2.9

3.x=9+root of 146(12.08) or x=9-root of 146

The matrix of A is [tex]A = \left[\begin{array}{ccc}0&0&-6\\9&0&0\\0&0&0\end{array}\right][/tex]

Let's start by considering the first standard basis vector [1 0 0]. Applying the transformation T to this vector gives:

T([1 0 0]) = [0 9 -6] * [1 0 0] = [0 0 0]

Therefore, the image of [1 0 0] under T is the zero vector [0 0 0]. Since the image of the first standard basis vector is the first column of the matrix A, we know that the first column of A is the zero vector.

We can follow the same process to find the image of the second standard basis vector [0 1 0]:

T([0 1 0]) = [0 9 -6] * [0 1 0] = [0 9 0]

Therefore, the image of [0 1 0] under T is the vector [0 9 0]. Since the image of the second standard basis vector is the second column of the matrix A, we know that the second column of A is [0 9 0].

Finally, we find the image of the third standard basis vector [0 0 1]:

T([0 0 1]) = [0 9 -6] * [0 0 1] = [-6 0 0]

Therefore, the image of [0 0 1] under T is the vector [-6 0 0]. Since the image of the third standard basis vector is the third column of the matrix A, we know that the third column of A is [-6 0 0].

Putting it all together, the matrix A of the linear transformation T (x) = v * x is:

[tex]A = \left[\begin{array}{ccc}0&0&-6\\9&0&0\\0&0&0\end{array}\right][/tex]

In conclusion, we can see that the matrix A captures how the linear transformation T maps each standard basis vector in R³. By applying this matrix to any vector in R³, we can efficiently compute the image of that vector under T.

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Okay, let's list the 4 rational numbers from smallest to largest:

5/3

7/15

6/10

25/5

So:

5/3 is A

7/15 is B

6/10 is C

25/5 is D

Answer:

3:5 or 3 to 5 or [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

[tex]\frac{6}{10}[/tex] ÷[tex]\frac{2}{2}[/tex] = [tex]\frac{3}{5}[/tex]

Helping in the name of Jesus.

Answer:

D. 67 square inches

Step-by-step explanation:

16 inches in diameter is an 8 inch radius. The area of a circle (the whole pizza) is

A = pi• r^2

= 3.14•8^2

= 64pi

= 200.96

The whole pizza is 200.96 square inches of pizza.

There are 12 pieces.

200.96 ÷ 12

= 16.746666...

Each slice is 16.75 sq inches.

The guys ate 4 pieces each.

16.75 × 4

= 67

Each guy ate 67 sq inches of pizza.

Union will need to choose a random sample of at least 65 wages to be 90% confident that its estimate of the mean hourly wage of foodservice workers is within $0.45 of the true population mean.

To calculate the minimum sample size needed for the union to be 90% confident within $0.45 of the true population mean, we can use the formula which states n = (Z^2 * σ^2) / E^2

Z = 90% = 1.645

σ = $2.20

E = $0.45

Substituting the values, we get:

n = (1.645^2 * 2.20^2) / 0.45^2

n = 13.097161 / 0.2025

n = 64.6773382716

n = 64.678

n = 65

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Answer:

C. -3x + 2y = 20

Step-by-step explanation:

Since the slope of line P is -2/3, and line Q is perpendicular to line P, the slopes of lines P and Q will be negative reciprocals. So the slope of line Q is 3/2. Since (-6, 1) is on line Q, we have:

1 = (3/2)(-6) + b

1 = -9 + b

b = 10

y = (3/2)x + 10

2y = 3x + 20

-3x + 2y = 20, so the correct answer is C.

The final product of the given algebraic expression is: b⁴ - 64

Algebraic expressions are defined as simply the idea of expression of numbers using letters without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as a, b, c, etc. These letters are referred to as variables. An algebraic expression can be a combination of both the variables and the constants. Any value that is placed before and multiplied by a variable is a coefficient.

The expression is given as:

(b² + 8)(b² - 8)

Expand the expression using (a + b)(a - b) = a² - b²

Thus:

(b² + 8)(b² - 8) = b⁴ - 64

Thus, that is the final product of the given algebraic expression.

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The measure of the angle ∠6 is 102 degrees for the given parallel lines.

Two angles are said to be supplementary if their sums equal 180 degrees. In other words, if angles A and B are complementary, then the sum of the two angles is 180 degrees. Four angles are created when two lines intersect; if two of these angles are supplementary, the other two are likewise supplementary.

Since 70 + 110 = 180 degrees, 70 degrees and 110 degrees serve as an illustration of a pair of supplementary angles. Another illustration is a pair of vertical angles, which are always supplementary and are generated by the intersection of two lines.

The measure of angle of a straight line is given as 180 degrees.

Thus,

∠6 + 78 = 180

∠6 = 180 - 78

∠6 = 102

Hence, the measure of the angle ∠6 is 102 degrees for the given parallel lines.

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Answer:

14. D) x+25=50; when x=157, x+25=182, which is equal to 50.

15. a) 3; you can solve for r by isolating the variable on one side of the equation. First, add 21 to both sides to get 10g - 21 + 21 = 7r + 12 + 21. Simplify to get 10g = 7r + 33. Then, subtract 33 from both sides to get 10g - 33 = 7r. Finally, divide both sides by 7 to get r = (10g - 33)/7. Plugging in a value for g, such as 3, gives you r = 3.

16. C) 2; combine like terms on both sides of the equation to get r - 8 = 8r + 10. Then, isolate the variable by subtracting r from both sides to get -9r - 8 = 10. Next, add 8 to both sides to get -9r = 18. Finally, divide both sides by -9 to get r = -2.

17. a) -36; start by isolating the variable on one side of the equation. Add 18 to both sides to get m/3 = m + 24. Then, subtract m from both sides to get -2m/3 = 24. Next, multiply both sides by -3/2 to get m = -36.

Step-by-step explanation:

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The perfect square is the integer that can be expressed as the square of another integer. Moreover, it is said to be the product of some integer with itself.

To see the percent of the perfect squares less than 1000 that end in a 6. Let us see the perfect squares under 1000.

Perfect squares  < 1000

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256. 289, 324, 361, 400. 441. 484, 529. 576, 625, 676, 729, 784, 841, 900, 961

Hence, there are 32  perfect squares less than 1000 in which,

6  end  in a "6"

So

6  / 32 = 3/ 16   = 18.75 %

Therefore 18.75% percent of the perfect squares are less than 1000 that end in a 6.

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Answer:

X = -8 X= -4

Step-by-step explanation:

x² + 12x = -32

(x + 12/2)² = -32 + (12/2)²

(x + 6)²= 4

square root both sides

x + 6 = 2

x + 6 = -2

x=-8 x=-4

The surface area of a rectangular prism is the sum of the areas of all its faces. The answer is B) two hundred two and fourteen twenty-fifths cm²

Surface area refers to the total area occupied by the surface of an object. It is found by adding up the areas of all the faces or surfaces of the object. For example, the surface area of a cube is found by multiplying the length of one edge by itself, and then multiplying the result by six, since a cube has six faces of equal area.

A rectangular prism is a three-dimensional solid shape that has six faces, where each face is a rectangle. It is also known as a rectangular parallelepiped.

According to given information :

To find the surface area of the rectangular prism, we need to find the area of each face and then add them together. Using the given dimensions, we can see that the six faces have areas of:

Front and back faces: 7 cm x 2 and 2/5 cm = 29 and 3/5 square cm each

Top and bottom faces: 3 and 3/5 cm x 2 and 2/5 cm = 9 and 9/25 square cm each

Side faces: 7 cm x 3 and 3/5 cm = 25 and 1/5 square cm each

Adding these areas together, we get a total surface area of:

2(29 and 3/5) + 2(9 and 9/25) + 2(25 and 1/5)

= 59 and 1/5 + 18 and 18/25 + 50 and 2/5

= 127 and 11/25 square cm

Therefore, the closest answer to the surface area of the prism is B) two hundred two and fourteen twenty-fifths cm²

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Answer:

The answer is C. 24, 9, -11, -24, -33.

In this list, 24 is the greatest integer, followed by 9, then -11, then -24, and finally -33. The other options are not in order from greatest to least.

Step-by-step explanation:

Answer:

The answer is C. 24, 9, -11, -24, -33.

In this list, 24 is the greatest integer, followed by 9, then -11, then -24, and finally -33. The other options are not in order from greatest to least.

Step-by-step explanation:

In 2022, Tom will have approximately 157783.78 in his account.

Future Value (FV)

= Principal (P) * (1 + Interest Rate (R))^Number of Years (N)

In this case:

Principal (P) = $100

Interest Rate (R) = 3.5%  = 0.035

Number of Years (N)

= 2022 - 1759

= 263 years

Now we can plug in the values into the formula:

FV = $100 * (1 + 0.035)^263

FV ≈ $100 * 1577.837835196 (rounded to 9 decimal places)

FV ≈ $157,783.78 (rounded to 2 decimal places)

So, in 2022, Tom will have approximately 157783.78 in his account.

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The correct representations of the inequality –3(2x – 5) < 5(2 – x) are x > 5 and x > 5

From the question, we have the following parameters that can be used in our computation:

–3(2x – 5) < 5(2 – x)

Open the brackets

So, we have

-6x + 15 < 10 - 5x

Evaluate the like terms

So, we have

-x < -5

This gives

x > 5

Hence, the correct representations of the inequality are x > 5 and x > 5

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If you started driving 10 miles closer to the beach then you normally would, after 2 hours of driving, you are 130 miles away from home.

Assuming that the distance to the beach from your home is "d" miles, you normally drive "d - 10" miles before reaching the beach.

If you drive for 2 hours at 70 miles per hour, you will have traveled a total distance of:

distance = speed x time = 70 x 2 = 140 miles

However, this distance includes the 10 miles that you started closer to the beach than normal. Therefore, the distance you have traveled from your home is:

distance from home = 140 - 10 = 130 miles

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The dimensions of the cubicle are 31.97 and 16.5 respectively.

We make diagram of rectangular office and AB is diagonal

let L be length and E be width

From the information, the diagonal of the floor of a rectangular office cubicle is 4 ft longer than the length of the cubicle and 3ft longer than twice the width.

As given  diagonal of the floor of a rectangular office cubicle is 4 ft longer than the length L.

So D = l + 4

D² = L² + W²

(D - 4)² + (D - 3)² / 4 = D²

Simplifying further, the dimensions of the cubicle are 31.97 and 16.5 respectively.

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